EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-EP-2018-149 2018/12/03
CMS-SUS-17-003
Search for supersymmetry in events with a τ lepton pair
and missing transverse momentum in proton-proton
collisions at
√
s
=
13 TeV
The CMS Collaboration
∗Abstract
A search for the electroweak production of supersymmetric particles in proton-proton collisions at a center-of-mass energy of 13 TeV is presented in final states with a τ lepton pair. Both hadronic and leptonic decay modes are considered for the τ lep-tons. Scenarios involving the direct pair production of τ sleptons, or their indirect production via the decays of charginos and neutralinos, are investigated. The data correspond to an integrated luminosity of 35.9 fb−1 collected with the CMS detector in 2016. The observed number of events is consistent with the standard model back-ground expectation. The results are interpreted as upper limits on the cross section for τ slepton pair production in different scenarios. The strongest limits are observed in the scenario of a purely left-handed low mass τ slepton decaying to a nearly mass-less neutralino. Exclusion limits are also set in the context of simplified models of chargino-neutralino and chargino pair production with decays to τ leptons, and range up to 710 and 630 GeV, respectively.
Published in the Journal of High Energy Physics as doi:10.1007/JHEP11(2018)151.
c
2018 CERN for the benefit of the CMS Collaboration. CC-BY-4.0 license
∗See Appendix B for the list of collaboration members
1
1
Introduction
Supersymmetry (SUSY) [1–8] is an attractive extension of the standard model (SM) of particle physics. It potentially provides solutions to some of the shortcomings affecting the SM, such as the need for fine tuning [9–14] to explain the observed value of the Higgs boson mass [15–20], and the absence of a dark matter (DM) candidate. Supersymmetric models are characterized by the presence of a superpartner for every SM particle with the same quantum numbers ex-cept that its spin differs from that of its SM counterpart by half a unit. The cancellation of quadratic divergences in quantum corrections to the Higgs boson mass from SM particles and their superpartners could resolve the fine-tuning problem. In SUSY models with R-parity con-servation [21], the lightest supersymmetric particle (LSP) is stable [22, 23] and could be a DM candidate [24]. The superpartners of the electroweak gauge and Higgs bosons, namely the bino, winos, and Higgsinos, mix to form neutral and charged mass eigenstates, referred to as the neutralinos (χe
0
i) and charginos (χe ±
i ), respectively. In this paper we assumeχe
0
1, the lightest
neutralino, to be the LSP.
The analysis reported in this paper investigates the production of the hypothetical τ slepton (eτ), the superpartner of the τ lepton. Supersymmetric scenarios in which theeτis light lead to the possibility of τ lepton rich final states [25, 26]. Coannihilation scenarios involving a lightτe that has a small mass splitting with an LSP that is almost purely bino lead to a DM relic density consistent with cosmological observations [27–32], making the search for new physics in these final states particularly interesting. In this analysis, we examine simplified SUSY models [33– 36] in which theτecan be produced either directly, through pair production, or indirectly, in the decay chains of charginos and neutralinos. In all cases, we assume that theeτdecays to a τ lepton andχe
0
1. The most sensitive searches for directτepair production to date were performed at the CERN LEP collider [37–41]. At the CERN LHC, the ATLAS [42, 43] and CMS [44, 45] Collaborations have both performed searches for direct and indirectτeproduction with 8 TeV LHC data. The ATLAS Collaboration has also recently reported the results of a search for SUSY in final states with τ leptons, probing indirectτeproduction in models of chargino-neutralino and chargino pair production, using data collected at√s=13 TeV [46].
The cross section for directτepair production depends strongly on the chirality of the SM part-ner [47], while the experimental acceptance also changes considerably due to differences in the polarization of the τ leptons. We use the terms left- or right-handedeτto refer to aeτthat is the superpartner of a left- or handed chiral state, respectively. In the case of a purely right-handed τe, the decay products of hadronically decaying τ leptons originating from τedecays have larger visible transverse momentum (pT) than in the purely left-handed scenario, while
the reverse is true for leptonically decaying τ leptons. Three different scenarios of direct τe pair production are considered in this paper: (i) a purely left-handedτe(τeL), (ii) a purely right-handed eτ(τeR), and (iii) maximal mixing between the right- and left-handed eigenstates. We also consider simplified models of mass-degenerate chargino-neutralino (χe
± 1 χe 0 2) and chargino pair (χe ± 1 χe ∓
1) production. We assume thatχe
0
2 (the second-lightest neutralino mass eigenstate)
decays through the chain χe
0
2 → ττe → ττχe
0
1, and that χe ±
1 (the lightest chargino) decays as
e
χ±1 → eτντ/eνττ→ τντχe
0
1, with equal branching fractions assumed for each of the two possible
e
χ±1 decay chains. For these indirect τeproduction mechanisms, we assume the eτto be in the maximally mixed state, and the degenerateeτandeντ masses to be halfway between the mass of the produced particles (χe
±
1/χe
0
2) and theχe
0
1mass. Diagrams illustrating these simplified models
of direct and indirecteτproduction are shown in Fig. 1.
The results reported in this paper are based on data collected with the CMS detector at the LHC during 2016 in proton-proton (pp) collisions at a center-of-mass energy of 13 TeV,
correspond-ing to an integrated luminosity of 35.9 fb−1. We study events with two τ leptons in the final state, taking into account both hadronic and leptonic decay modes of the τ lepton. The follow-ing reconstructed visible final states are considered: eµ, eτh, µτh, and τhτh, where τhdenotes a
hadronically decaying τ lepton. For the purposes of this paper, we will occasionally refer to the
τhτhfinal state as the all-hadronic final state, and the eµ, eτh, and µτhfinal states collectively as
the leptonic final states. In most cases, we require the presence of significant missing transverse momentum, which can arise from the presence of stable neutralinos produced at the end of the SUSY particle decay cascades, as well as from the neutrinos produced in τ lepton decays.
p p eτ e τ∗ τ+ e χ01 e χ01 τ− p p χe02 e χ±1 e τ e τ ν τ e χ01 e χ01 τ τ p p χe±1 e χ∓1 e τ e τ ν τ e χ01 e χ01 τ ν
Figure 1: Diagrams for the simplified models studied in this paper: directτepair production followed by eacheτdecaying to a τ lepton andχe
0
1(left), and chargino-neutralino (middle) and
chargino pair (right) production with subsequent decays leading to τ leptons in the final state. The structure of this paper is as follows. A brief description of the CMS detector is presented in Section 2, followed by a discussion of the event reconstruction and simulation in Section 3. We describe the event selection for the search in Section 4, the background estimation strategy in Section 5, and the systematic uncertainties affecting the analysis in Section 6. Finally, the results of the search and their statistical interpretation are presented in Section 7, followed by a summary in Section 8.
2
The CMS detector
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diame-ter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter, each composed of a barrel and two endcap sections. Forward calorimeters extend the pseudorapidity (η) coverage provided by the barrel and endcap detectors. Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid. Events of interest are selected using a two-tiered trigger system [48]. The first level, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100 kHz within a time interval of less than 4 µs. The second level, known as the high-level trigger, consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing, and reduces the event rate to around 1 kHz before data storage. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [49].
3
Event reconstruction and simulated samples
Event reconstruction uses a particle-flow (PF) algorithm [50], combining information from the tracker, calorimeter, and muon systems to identify charged and neutral hadrons, photons, elec-trons, and muons in an event. The missing transverse momentum,~pTmiss, is computed as the
3
negative vector sum of the pT of all PF candidates reconstructed in an event, and its
magni-tude pmissT is an important discriminator between signal and SM background. Events selected for the search are required to pass filters [51] designed to remove detector- and beam-related noise and must have at least one reconstructed vertex. Usually more than one such vertex is reconstructed, due to pileup, i.e., multiple pp collisions within the same or neighboring bunch crossings. The reconstructed vertex with the largest value of summed physics-object p2T is se-lected to be the primary pp interaction vertex. The physics objects are the jets, clustered using a jet finding algorithm [52, 53] with the tracks assigned to the vertex as inputs, and the associated
~pTmiss.
Charged particles that originate from the primary vertex, photons, and neutral hadrons are clustered into jets using the anti-kT algorithm [52] with a distance parameter of 0.4, as
imple-mented in the FASTJET package [53]. The jet energy is corrected to account for the contribu-tion of addicontribu-tional pileup interaccontribu-tions in an event and to compensate for variacontribu-tions in detector response [53, 54]. Jets considered in the searches are required to have their axes within the tracker volume, within the range|η| <2.4. We also require them to have pT >20 GeV. Jets are
required to be separated from electron, muon, or τhcandidates that are selected for the analysis
by∆R≡√(∆η)2+ (∆φ)2>0.4 in order to avoid double counting of objects.
Jets originating from the hadronization of b quarks are identified, or “tagged”, with the com-bined secondary vertex (CSV) algorithm [55, 56] using two different working points, referred to as “loose” and “medium”. The b tagging efficiency for jets originating from b quarks is measured in simulation to be about 81 (63)% for the loose (medium) working point, while the misidentification rates for jets from charm quarks, and from light quarks or gluons, are about 37 and 9% (12 and 1%), respectively.
Electron candidates are reconstructed by first matching clusters of energy deposited in the ECAL to reconstructed tracks. Selection criteria based on the distribution of the shower shape, track–cluster matching, and consistency between the cluster energy and track momentum are then used in the identification of electron candidates [57]. Muon candidates are reconstructed by requiring consistent measurement patterns in the tracker and muon systems [58]. Electron and muon candidates are required to be consistent with originating from the primary vertex by imposing restrictions on the magnitude of the impact parameters of their tracks with respect to the primary vertex in the transverse plane (dxy), and on the longitudinal displacement (dz)
of those impact points. To ensure that the electron or muon candidate is isolated from any jet activity, the relative isolation quantity (Irel), defined as the ratio of the scalar pT sum of the
particles in an η–φ cone around the candidate to the candidate pT, is required to be below a
threshold appropriate for the selection under consideration. An area-based estimate [54] of the pileup energy deposition in the cone is used to correct Irel for contributions from particles
originating from pileup interactions.
The τh candidates are reconstructed using the CMS hadron-plus-strips algorithm [59, 60]. The
constituents of the reconstructed jets are used to identify individual τ lepton decay modes with one charged hadron and up to two neutral pions, or three charged hadrons. The presence of extra particles within the jet, not compatible with the reconstructed decay mode, is used as a criterion to discriminate τh decays from other jets. A multivariate discriminant [61], which
contains isolation as well as lifetime information, is used to suppress the rate for quark and gluon jets to be misidentified as τhcandidates. The working point used for the analysis in the
eτh and µτh final states, referred to as the “tight” working point, typically has an efficiency
of around 50% for genuine τh, with a misidentification rate of approximately 0.03% for
the τhτhfinal state in order to suppress the background from SM events comprised uniquely of
jets produced through the strong interaction, referred to as quantum chromodynamics (QCD) multijet events. The very tight working point corresponds to typical efficiencies of around 40% for genuine τh, and a misidentification rate of approximately 0.01% for light-quark or gluon jets. We also employ a relaxed (“loose”) working point in the extrapolation procedures used to estimate the contributions of events to the background in which light-quark or gluon jets are misidentified as τh. The loose working point corresponds to an efficiency of ≈65% for
genuine τh, and a misidentification rate of≈0.07%. Electrons and muons misidentified as τh
are suppressed using dedicated criteria based on the consistency between the measurements in the tracker, calorimeters, and muon detectors [60, 61].
Significant contributions to the SM background for this search originate from Drell-Yan+jets (DY+jets), W+jets, tt, and diboson processes, as well as from QCD multijet events. Smaller contributions arise from rare SM processes such as triboson and Higgs boson production, single top quark production, and top quark pair production in association with vector bosons. We rely on a combination of data control samples and Monte Carlo (MC) simulations to estimate the contributions of each background source. MC simulations are also used to model the signal processes.
The MADGRAPH5 aMC@NLO 2.3.3 [62] event generator is used at leading order (LO) pre-cision to produce simulated samples of the W+jets and DY+jets processes, based on the NNPDF3.0LO [63] set of parton distribution functions (PDFs). Top quark pair production, di-boson and tridi-boson production, and rare SM processes like single top production or top quark pair production with associated bosons, are generated at next-to-leading order (NLO) preci-sion with MADGRAPH5 aMC@NLO andPOWHEGv2.0 [64–67], using the NNPDF3.0NLO [63] set of PDFs. Showering and hadronization are carried out by the PYTHIA8.205 package [68], while a detailed simulation of the CMS detector is based on the GEANT4 [69] package. Finally, renormalization and factorization scale and PDF uncertainties have been derived with the use of the SYSCALCpackage [70].
Signal models of directτepair production are generated with MADGRAPH5 aMC@NLOat LO precision up to the production of τ leptons, which are then decayed withPYTHIA8.212. For the models of chargino-neutralino pair production that are also studied,PYTHIA8.212 is used to de-scribe the decays of the parent charginos and neutralinos produced by MADGRAPH5 aMC@NLO at LO precision. The NNPDF3.0LO set of PDFs is used in the generation of all signal models. The CMS fast simulation package [71] is used to simulate the CMS detector for the signal sam-ples.
Event reconstruction in simulated samples is performed in a similar manner as for data. A nominal distribution of pileup interactions is used when producing the simulated samples. The samples are then reweighted to match the pileup profile observed in the collected data. The signal production cross sections are calculated at NLO with next-to-leading logarithmic (NLL) soft-gluon resummation calculations [47, 72, 73]. The most precise cross section calculations that are available are used to normalize the SM simulated samples, corresponding most often to next-to-next-to-leading order (NNLO) accuracy.
4
Event selection
The data used for this search are selected with various triggers that require the presence of isolated electrons, muons, or τhcandidates. In the case of the eτh final state, the trigger used
identifica-5
tion criteria, while for the µτh final state, the trigger is based on the presence of an isolated
muon with pT > 24 GeV. A combination of triggers is used for the events selected in the eµ
final state, requiring the presence of an electron and a muon. These triggers require the leading lepton to have pT greater than 23 GeV and the subleading lepton to have pT greater than 8 or
12 GeV for an electron or muon, respectively. Data in the τhτh final state are selected with a
trigger requiring the presence of two τhcandidates, each with pT >35 GeV. Trigger efficiencies
are measured in data and simulation. We apply scale factors accounting for any discrepancies, parameterized in the pT and η of the reconstructed electrons, muons, and τhcandidates, to the
simulation. The efficiencies measured in data are applied directly as correction factors to simu-lated signal samples, which are produced using the fast simulation package and for which the trigger simulation is not available. The trigger efficiencies range from 60 to 95%, depending on the final state and the pTand η range under consideration.
Subsequent to the trigger criteria, the event selection for each final state requires the presence of exactly two reconstructed leptons with opposite charges, corresponding to the eµ, eτh, µτh,
or τhτhfinal states. The various lepton selection requirements implemented in the analysis are
summarized in Table 1. The pT and|η|thresholds implemented when selecting these objects
are dictated by the corresponding trigger thresholds described above. We require all selected leptons to be isolated. In the case of electron and muon candidates, the isolation requirement is enforced by placing an upper bound on the relative isolation quantity, Irel. For τhcandidates, we use a multivariate discriminant. In order to ensure consistency with the primary vertex, upper bounds are placed on the absolute values of the electron and muon dxyand dz. We avoid
overlaps between the two reconstructed leptons in the mixed final states (eµ, eτh, and µτh)
by requiring them to have a minimum separation in∆R of at least 0.3. In order to ensure or-thogonality between the different final states and suppress background, we reject events with additional electrons or muons beyond the two selected leptons that satisfy slightly less strin-gent selection criteria. These criteria are summarized in Table 2.
Table 1: Summary of lepton selection requirements for the analysis. Entries with a second value in parentheses refer to the lepton with the higher (lower) pT.
Selection requirement eµ eτh µτh τhτh
Electron pT[GeV] >24(13) >26 — — Electron|η| <2.5 <2.1 — — Electron|dxy|[cm] <0.045 <0.045 — — Electron|dz|[cm] <0.2 <0.2 — — Electron Irel <0.1 <0.1 — — Muon pT[GeV] >24(10) — >25 — Muon|η| <2.4 — <2.4 — Muon|dxy|[cm] <0.045 — <0.045 — Muon|dz|[cm] <0.2 — <0.2 — Muon Irel <0.15 — <0.15 — τh pT[GeV] — >20 >20 >40 τh|η| — <2.3 <2.3 <2.1
τhisolation working point — Tight Tight Very tight
A subsequent set of selection criteria is imposed for each final state to further suppress back-ground and enhance the search sensitivity. Differences in the backback-ground compositions be-tween the different final states play a role in the determination of the corresponding selection criteria which, together with the selection requirements described above, define the “baseline selection”.
Table 2: Summary of requirements for identifying additional electrons and muons.
Selection requirement eµ eτh µτh τhτh
Electron pT[GeV] >15 >15 >10 >20 Electron|η| <2.5 <2.5 <2.5 <2.5 Electron|dxy|[cm] <0.045 <0.045 <0.045 <0.1 Electron|dz|[cm] <0.2 <0.2 <0.2 <0.2 Electron Irel <0.3 <0.3 <0.3 <0.175 Muon pT[GeV] >15 >10 >15 >20 Muon|η| <2.4 <2.4 <2.4 <2.4 Muon|dxy|[cm] <0.045 <0.045 <0.045 <0.045 Muon|dz|[cm] <0.2 <0.2 <0.2 <0.2 Muon Irel <0.3 <0.3 <0.3 <0.25
In all final states, we require|∆φ(`1,`2)| >1.5, with additional requirements of∆R(`1,`2) <3.5
and|∆η(`1,`2)| < 2 being applied for the leptonic final states to suppress the QCD multijet
background. Here`1and`2represent the leading and trailing reconstructed electrons, muons, or τh candidates, respectively. In order to suppress backgrounds with top quarks, we veto
events containing any b-tagged jet with pT > 30 GeV identified with the loose CSV working
point in the τhτh final state. In the leptonic final states, these backgrounds are reduced by
vetoing any event that contains either more than one jet with pT > 20 GeV, or any such jet
that is b tagged using the medium CSV working point. One-jet events in these final states are required to have a separation in|∆η|of less than 3 between the jet and the reconstructed leptons and, in the case of the eτh and µτh final states, a separation in ∆R of less than 4 between the
jet and the τh. Background events from low-mass resonances are removed in these final states
by requiring the invariant mass of the two leptons, m(`1,`2), to exceed 50 GeV. In the eµ final state, m(`1,`2)is required to lie in the window 90–250 GeV in order to suppress Z+jets events with Z → ττ, while the electron and muon pT are required to be less than 200 GeV in order
to suppress tt and WW events, since the signal processes targeted are not expected to produce leptons with higher pT.
In order to further improve discrimination against the SM background, we take advantage of the expected presence of two χe
0
1 in the final state for signal events, which would lead to
additional pmissT . While background processes such as W+jets with W → `νcan also produce
genuine pmissT , the correlations between~pTmiss and the reconstructed leptons are expected to be different between signal and background processes, and these differences can be exploited. In particular, mass observables that can be calculated from the reconstructed leptons and the~pmiss
T
provide strong discriminants between signal and background. For a mother particle decaying to a visible and an invisible particle, the transverse mass (mT), calculated using only the~pT
of the decay products, should have a kinematic endpoint at the mass of the mother particle. Assuming that the pmissT corresponds to the pT of the invisible particle, we calculate the mT
observable for the visible particle q and the invisible particle as follows:
mT(q,~pTmiss) ≡
q
2pT,qpmissT [1−cos∆φ(~pT,q,~pTmiss)]. (1)
By requiring 20< mT(`,~pTmiss) <60 GeV or mT(`,~pTmiss) >120 GeV where`here represents the
electron (muon) in the eτh(µτh) final state, the W+jets background is significantly reduced. To
further suppress the SM background in the leptonic final states, we require the sum of the trans-verse masses,ΣmT, to be at least 50 GeV. TheΣmTis defined as the scalar sum of mT(`1,~pTmiss)
and mT(`2,~pTmiss).
cri-7
teria to obtain an optimized sample of events in each final state. These events are then further subdivided using discriminating kinematic variables into exclusive search regions (SRs) to im-prove the sensitivity of the search to a range of sparticle masses. One of these discriminating variables is the “stransverse mass” mT2 [74, 75]. This kinematic mass variable is a
generaliza-tion of the variable mTfor situations with multiple invisible particles. It serves as an estimator
of the mass of pair-produced particles in situations in which both particles decay to a final state containing the same invisible particle. For directτepair production, with bothτedecaying to a
τlepton and aχe
0
1, mT2should be correlated with theτemass. Large values of mT2can therefore be used to discriminate between models with large eτ masses and the SM background. This variable is again calculated using the~pTof the different particles:
mT2 = min
~pTX(1)+~pTX(2)=~pmiss T
h
maxm(T1), m(T2)i, (2)
where~pTX(i)(with i=1,2) are the unknown transverse momenta of the two undetected particles and m(Ti)are the transverse masses obtained by either pairing of the two hypothetical invisible particles with the two leptons. The minimization is done over the possible momenta of the invisible particles, which should add up to the~pTmissin the event.
Another variable that is used to distinguish signal from background, Dζ, is defined as:
Dζ = Pζ,miss−0.85Pζ,vis, (3)
where Pζ,miss = ~pTmiss· ~ζ and Pζ,vis = (~p
`1
T + ~p
`2
T ) · ~ζ, with~ζ being the bisector between the
directions of the two leptons. The Dζ variable helps to discriminate events in which pmissT originates from the decay of two τ leptons from other processes [76, 77]. Different background processes are characterized by different ranges of Dζ. For instance, the DY+jets background is largely expected to have positive Dζ values, while W+jets and tt events may have negative values.
The more restrictive trigger requirements in the τhτh final state significantly reduce the signal
acceptance, and the very low cross sections of the targeted eττesignal models result in very small expected signal event yields after the baseline selection. Events surviving the baseline selection in this final state are therefore categorized into only three SRs. These three SRs are exclusive and are optimized for sensitivity to different eτ mass ranges. For higher values of theeτmass, a requirement of large mT2significantly improves the discrimination of signal from background. We therefore define a search region, designated SR1, by selecting events with
Table 3: Summary of baseline selection requirements in each final state.
Selection requirement eµ eτh µτh τhτh
|∆φ(`1,`2)| >1.5 >1.5 >1.5 >1.5
|∆η(`1,`2)| <2 <2 <2 —
∆R(`1,`2) <3.5 <3.5 <3.5 —
b-tagged jet veto pT>20 GeV, pT>20 GeV, pT>20 GeV, pT>30 GeV,
medium CSV medium CSV medium CSV loose CSV
Additional jet veto >1 jet, pT>20 GeV >1 jet, pT>20 GeV >1 jet, pT>20 GeV —
|∆η(jet,`i)|(1–jet events) <3 <3 <3 —
∆R(jet, τh)(1–jet events) — <4 <4 —
m(`1,`2)[GeV] 90–250 >50 >50 —
e/µ pTupper bound [GeV] <200 — — —
mT(e/µ,~pTmiss)[GeV] —
20–60 20–60
— or>120 or>120
mT2 >90 GeV. For lowereτmasses,ΣmTis found to be a more powerful discriminant than mT2. Two additional SRs, designated SR2 and SR3, are therefore defined by selecting events with moderate mT2 (40 < mT2 < 90 GeV), and further subdividing them into high and moderate
ΣmT ranges: >350 GeV and 300–350 GeV, respectively. For these two SRs, we place a further
requirement of pmissT >50 GeV to sufficiently suppress the QCD multijet background.
In the leptonic final states, events satisfying the baseline selection criteria are categorized into SRs based on a series of thresholds applied to the values of the discriminating observables pmissT , mT2, and Dζ. The SR binning is defined to be slightly different for events in the 0- and 1-jet categories and is chosen such that there are small variations in the relative background contributions in the different bins. This allows us to obtain stronger constraints on the back-ground predictions in the final result, obtained from a simultaneous maximum likelihood fit to the data in all SRs. Tables 4 to 7 list the criteria used to define the SRs in the 0- and 1-jet categories, respectively. While the same binning is chosen for the eτh and µτhfinal states, the
SR bins chosen in the eµ final state are slightly different because of the different background composition.
Table 4: Definition of SRs in the 0-jet category for the eτhand µτhfinal states.
Bin name pmiss
T [GeV] mT2[GeV] Dζ [GeV]
0j−1 <40 <40 < −100 0j−2 >40 > −500 0j−3 [40,80] <40 < −100 0j−4 >50 0j−5 [40,80] < −100 0j−6 > −100 0j−7 >80 > −500 0j−8 [80,120] <40 < −100 0j−9 > −100 0j−10 [40,80] < −150 0j−11 > −150 0j−12 >80 > −500 0j−13 [120,250] <40 < −100 0j−14 > −100 0j−15 [40,80] < −150 0j−16 [−150,−100] 0j−17 > −100 0j−18 [80,100] > −500 0j−19 [100,120] > −500 0j−20 >120 > −500 0j−21 >250 >0 > −500
5
Background estimation
The dominant background sources for this search are DY+jets, W+jets, QCD multijet, tt, and diboson processes. These background sources have different relative contributions in the dif-ferent final states. For the τhτhfinal state, the dominant background consists of QCD multijet
and W+jets processes, where one or more of the τhcandidates originates from a parton and is
9
Table 5: Definition of SRs in the 1-jet category for the eτhand µτhfinal states.
Bin name pmissT [GeV] mT2[GeV] Dζ [GeV]
1j−1 <40 <40 < −150 1j−2 [−150,100] 1j−3 >40 > −500 1j−4 [40,80] <40 < −100 1j−5 >50 1j−6 [40,80] < −100 1j−7 > −100 1j−8 >80 > −500 1j−9 [80,120] <40 < −100 1j−10 [40,80] < −150 1j−11 > −150 1j−12 [80,120] > −500 1j−13 >120 > −500 1j−14 [120,250] <40 < −150 1j−15 [−150,−100] 1j−16 > −100 1j−17 [40,80] < −150 1j−18 [−150,−100] 1j−19 > −100 1j−20 [80,100] > −500 1j−21 [100,120] > −500 1j−22 >120 > −500 1j−23 >250 >80 > −500
Table 6: Definition of SRs in the 0-jet category for the eµ final state. Bin name pmissT [GeV] mT2[GeV] Dζ [GeV]
0j−1 <40 <40 < −100 0j−2 >0 0j−3 >40 > −500 0j−4 [40,80] <40 < −100 0j−5 >50 0j−6 [40,80] < −100 0j−7 > −100 0j−8 >80 > −500 0j−9 [80,120] <40 < −100 0j−10 > −100 0j−11 [40,80] < −150 0j−12 > −150 0j−13 >80 > −500 0j−14 [120,250] <40 < −100 0j−15 > −100 0j−16 [40,80] < −150 0j−17 [−150,−100] 0j−18 > −100 0j−19 [80,100] > −500 0j−20 [100,120] > −500 0j−21 >120 > −500 0j−22 >250 >0 > −500
11
Table 7: Definition of SRs in the 1-jet category for the eµ final state. Bin name pmissT [GeV] mT2[GeV] Dζ [GeV]
1j−1 <40 <40 < −150 1j−2 [−150,100] 1j−3 >0 1j−4 >40 > −500 1j−5 [40,80] <40 < −100 1j−6 >50 1j−7 [40,80] > −100 1j−8 >40 > −500 1j−9 [80,120] <40 < −100 1j−10 [40,80] < −100 1j−11 [80,120] > −500 1j−12 >120 > −500 1j−13 [120,250] <40 < −150 1j−14 [−150,−100] 1j−15 > −100 1j−16 [40,80] < −150 1j−17 [−150,−100] 1j−18 > −100 1j−19 [80,100] > −500 1j−20 [100,120] > −500 1j−21 >120 > −500 1j−22 >250 >80 > −500
on a control region with a loose isolation requirement. For the eτhand µτhfinal states, the main
backgrounds after the baseline selection are DY+jets (≈50%), W+jets (≈30%), and QCD multijet (≈10%) events. The DY+jets background contribution, which usually consists of events with two prompt leptons, is determined from simulation after applying shape and normalization corrections that are determined from data. The W+jets and QCD multijet backgrounds usually contain a jet that is misidentified as τh, and are determined from a sideband sample using a
data-driven method similar to the one used in the τhτhcase. The main backgrounds in the eµ
final state originate from tt (≈45%) and WW (≈35%) events, and are estimated from simulation after applying corrections derived from data. A detailed description of the procedures used to estimate the background contributions from the different sources follows.
5.1 Estimation of the Drell-Yan+jets background
The DY+jets background mainly originates from Z→ττdecays. We estimate the contribution
of this background from simulation after corrections based on control samples in data. If the Z boson mass shape or pT spectrum are poorly modeled in the simulation, then distributions
of the discriminating kinematic variables can differ significantly between data and simulation, especially at the high-end tails that are relevant for the SRs. We therefore use a high-purity Z→
µµ control sample to compare the dimuon mass and pT spectra between data and simulation
and apply the observed differences as corrections to the simulation in the search sample in the form of two-dimensional weights parameterized in the generator-level Z boson mass and pT. The correction factors range up to 30% for high mass and pT values. The full size of this
correction is propagated as a systematic uncertainty. The known differences in the electron, muon, and τhidentification and isolation efficiencies, jet, electron, muon, and τhenergy scales,
and b tagging efficiency between data and simulation are taken into account. The uncertainties corresponding to these corrections are also propagated to the final background estimate. The corrected simulation is validated in the τhτhfinal state using a Z→ττcontrol sample selected
by inverting either the mT2orΣmTrequirements used to define the SRs. Additionally requiring
a pTof at least 50 GeV for the τhτhsystem reduces the QCD multijet background and improves
the purity of this control sample. Figure 2 (left) shows that the corrected simulation agrees with the data within the experimental uncertainties in this sample.
Finally, for the analysis in the leptonic final states, a normalization scale factor as well as cor-rections to the Z pTdistribution in the simulation are derived from a very pure Z→µµcontrol
sample in data. Events in this sample are selected by requiring two isolated muons and no additional leptons, fewer than two jets, no b-tagged jets, and a dimuon mass window of 75– 105 GeV to increase the probability that they originate from Z → µµ decays to >99%. After
subtracting all other contributions estimated from simulation, a normalization scale factor of 0.96±0.05 is extracted from the ratio of data to simulated events. The uncertainty in the scale factor is dominated by the systematic uncertainty. Figure 2 (right) shows a comparison of the dimuon mass distribution in data and simulation after all the corrections, including the nor-malization scale factor, have been applied.
5.2 Estimation of the background from misidentified jets
5.2.1 Estimation in the τhτh final state
After requiring two high-pTτhcandidates, the dominant background for the search in the τhτh
final state consists of QCD multijet and W+jets events, in which one or both of the τhcandidates originate from a jet and are misidentified as prompt τh. This background is predicted using a
method relying on extrapolation from a data sample selected with a loose isolation require-ment. We estimate how frequently nonprompt or misidentified τhcandidates that are selected
5.2 Estimation of the background from misidentified jets 13 Entries / 10 GeV 1 10 2 10 3 10 4 10 5 10 h
τ
hτ
Observed Top quark
DY+jets Jet →τh Other SM ) [GeV] h τ , h τ m( 40 60 80 100 120 140 160 180 200 Obs. / MC 1 2 Syst. unc. (13 TeV) -1 35.9 fb CMS Entries / 1 GeV 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10
µ
µ
Observed Top quark
DY+jets Other SM ) [GeV] µ , µ m( 75 80 85 90 95 100 105 Obs. / MC 0.5 1 1.5 Syst. unc. (13 TeV) -1 35.9 fb CMS
Figure 2: Left: visible mass spectrum used to validate the modeling of the DY+jets background in the τhτhfinal state in a Z→ττcontrol sample selected with low mT2orΣmTand a minimum τhτhsystem pTof 50 GeV. The last bin includes overflows. Right: dimuon mass distribution in
the high-purity Z→µµcontrol sample after all estimated correction factors have been applied
to the simulation. In the legend, “Top quark” refers to the background originating from tt and single top quark production.
with the loose isolation working point also pass the very tight isolation requirement applied in the SRs by studying a multijet-enriched control sample where we require both τhcandidates to have the same charge. The same-charge τhτh event sample is collected with the same trigger
as the search sample, in order to take into account any biases from the isolation requirement present at the trigger level, which is not identical to the isolation requirement that corresponds to the final analysis selection criteria. We also require mT2to be small (<40 GeV) to reduce any
potential contributions from signal and W+jets events.
The final rate measured in this sample for misidentified τh selected with the loose isolation
working point to pass the very tight isolation requirement is around 25%, but it depends con-siderably on the pT and the decay mode (one- or three-prong) of the τh candidate, and the
parent jet flavor. The extrapolation is measured in bins of τhpTand separately for the different
decay modes to reduce any dependence on these factors. A systematic uncertainty of around 30% is evaluated that accounts for the dependence of the misidentification rate on the jet flavor, based on studies performed in simulation. We also noticed that the extrapolation is affected by whether or not the τhcandidate other than the one for which the extrapolation is being applied
is isolated. A correction and a corresponding systematic uncertainty are derived for this effect. Since the isolation efficiency for prompt τhcandidates is only around 65%, processes with gen-uine τhmay leak into the data sideband regions and need to be taken into account when
cal-culating the final estimate for the background processes with misidentified τh. To take this
cor-rectly into account, we define three categories for events that have at least two loosely isolated
τh candidates: events with both τh candidates passing the very tight isolation requirement,
events with one passing and one failing the very tight isolation requirement, and finally events with both τhcandidates failing the very tight isolation requirement. We then equate these
ob-servable quantities with the expected sum totals of contributions from events with two prompt
can-didate to each of these populations. The contributions of background events with one or two misidentified τhcandidates in the SRs can then be determined analytically by inverting this set
of equations. A closure test is performed in events with two oppositely charged τhcandidates. where the mT2orΣmT requirements used to define the SRs are explicitly inverted to avoid any
overlap with the SRs. Figure 3 (left), which shows the mT2distribution in this sample, confirms
that the background estimation method is able to predict the background with misidentified τh
candidates within the systematic uncertainties.
5.2.2 Estimation in the eτh and µτh final states
The misidentification of jets as τh candidates also gives rise to a major source of background for the search in the eτhand µτhfinal states, mainly from W+jets events with leptonic W boson decays. We estimate this background from a sideband sample in data selected by applying the SR selections, with the exception that the τh candidates are required to satisfy the loose
but not the tight isolation working point. A transfer factor for the extrapolation in τhisolation
is determined from a W+jets control sample selected from events with one muon and at least one τh candidate that passes the loose isolation requirement. In events with more than one τh candidate, the most isolated candidate is used in the determination of the transfer factor.
Events with additional electrons or muons satisfying the criteria listed in Table 2 are rejected. In order to increase the purity of W+jets events in this sample by reducing the contribution of tt and QCD multijet events, we require 60 < mT < 120 GeV, pmissT > 40 GeV, no more than
two jets, and an azimuthal separation of at least 2.5 radians between any jet and the W boson reconstructed from the muon and the~pTmiss. The remaining sample has an expected purity of 82% for W+jets events. The transfer factor, R, is then determined from this control sample, after subtracting the remaining non-W+jets background contributions estimated from simulation, as follows:
R= N
CS
data(T) −NMC no WCS (T)
NdataCS (L&!T) −NMC no WCS (L&!T). (4) Here, NdataCS corresponds to the number of events in the control sample in data. The parentheti-cal arguments T and L&!T denote events in which the τh candidate satisfies the tight isolation
working point, and the loose but not the tight working point, respectively. The transfer factor is determined in bins of pTand η of the τhcandidate, as tabulated in Table 8.
Table 8: Transfer factor R determined from the W+jets control sample according to Eq. (4), as a function of pTand η of the τhcandidate. The uncertainties are statistical only.
(|η|, pT) 20–30 GeV 30–40 GeV >40 GeV
|η| <0.80 0.74±0.07 0.66±0.01 0.56±0.02
0.80< |η| <1.44 0.68±0.01 0.61±0.01 0.39±0.03
1.44< |η| <1.57 0.68±0.03 0.64±0.08
1.57< |η| <2.30 0.59±0.02 0.61±0.01
The contribution of the background originating from a jet misidentified as a τh candidate in
each SR is then determined from the corresponding data sideband region selected by requiring the τhcandidate to satisfy the loose but not the tight isolation working point as follows:
NSR(jet→τ) =R(Ndatasideband−NMCsideband(genuine τ)), (5)
where Nsideband
data represents the number of data events in the sideband region, from which
5.3 Estimation in theeµ final state 15
from simulation with generator-level matching, is subtracted. Figure 3 (middle) shows a com-parison of the data with the background prediction in the eτhfinal state for theΣmTdistribution
for the baseline selection, where the ratio of signal to background is expected to be small.
5.3 Estimation in the eµ final state
Jets may also be misidentified as electrons or muons, although the misidentification probabili-ties for these objects are smaller than for τh. The contribution of the background from
misiden-tified jets in the eµ final state is determined from data using a matrix method. For each SR selection we define four regions A, B, C, and D, which contain events with two leptons of ei-ther the same or opposite charge. We designate two categories for the leptons: well-isolated (electrons with Irel < 0.1, muons with Irel <0.15), or loosely-isolated (0.1 < Irel< 0.2 for
elec-trons, 0.15< Irel<0.30 for muons). In order to enrich the QCD multijet contribution in events
in the loosely-isolated category, we also invert the baseline selection requirements affecting the separation between the two leptons, i.e., we now require∆R(`1,`2) >3.5 and|∆η(`1,`2)| >2. We use the designations A (B) for the regions with two well-isolated leptons of the same (op-posite) charge, and C (D) for the corresponding regions with a loosely-isolated lepton. Region B constitutes the search region. The purity of the C and D regions in QCD multijet events is >90%, while that of the A regions is≈55% after the SR selections.
The charge and the isolation of misidentified leptons are expected to be uncorrelated. However, we expect a correlation to be present for the other backgrounds in these regions, e.g., prompt leptons from tt events are expected to have opposite charge. In order to account for this effect, we subtract the contributions expected from simulation for all other backgrounds from the observed numbers of events in the A, C, and D regions to obtain the estimate of the background originating from misidentified leptons in the SRs, NB, as follows:
NB = (NdataA −NAMC)
NDdata−NDMC Ndata
C −NCMC
. (6)
The distribution of the muon dz is shown in Fig. 3 (right) for events in the eµ final state and
illustrates the estimation of the QCD multijet background using the matrix method. The data agree well with the predicted background.
5.4 Estimation of other backgrounds
Smaller contributions exist from other SM backgrounds, including other diboson processes, such as WZ +jets, triboson, and Higgs boson processes. There are also contributions from top quark processes: tt and single top quark production, or top quark pair production in associ-ation with vector bosons. These are estimated from simulassoci-ation, using the known efficiency and energy scale corrections and evaluating both experimental and theoretical uncertainties as described in Section 6. The shape of the top quark pT spectrum is known to be different
between simulation and data from studies of the differential tt cross section [78, 79]. The sim-ulation is therefore reweighted by a correction factor parameterized in the top quark pT to
improve the modeling of the tt background, and the full size of the correction is propagated as a systematic uncertainty. The normalization of this background is checked in an eµ control sample enriched in tt events, selected by requiring the presence of at least two jets, at least one of which should be b tagged. The ratio of data to simulation for tt events is found to be 1.00±0.05 (syst)±0.01 (stat), i.e., consistent with unity.
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τ
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Observed Top quark
(1) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ DY+jets (175) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ Jet →τh (1) 0 1 χ∼ (90), L τ∼ Other SM [GeV] T2 m 0 10 20 30 40 50 60 70 80 Obs. / MC 1 2 Syst. unc. (13 TeV) -1 35.9 fb CMS Entries / 10 GeV 1 − 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 h
τ
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Observed Top quark
(1) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ DY+jets (175) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ Jet →τh (1) 0 1 χ∼ (90), L τ∼ Other SM [GeV] T m Σ 50 100 150 200 250 300 350 Obs. / MC 1 2 Syst. unc. (13 TeV) -1 35.9 fb CMS h τ µ Entries / 0.02 cm 1 − 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10
µ
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Observed Top quark
(1) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ WW+jets (175) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ QCD multijet (1) 0 1 χ∼ (90), L τ∼ Other SM ) [cm] µ ( z d 0.2 − −0.15−0.1−0.05 0 0.05 0.1 0.15 0.2 Obs. / MC 1 2 Syst. unc. (13 TeV) -1 35.9 fb CMS
Figure 3: Top left: closure test for the method used to estimate the τh misidentification rate
for the τhτhfinal state in a data control sample where the mT2orΣmTrequirements used in the
SRs are inverted. Top right: ΣmTdistribution for events in the eτhfinal state after the baseline
selection, showing the estimation of the background with a jet misidentified as a τh, which is
determined in a signal depleted control region. The last bin includes overflows. Bottom: distri-bution of the muon dzin the eµ final state after the baseline selection, showing the estimation
of the QCD multijet background using the matrix method. In the legend,“Top quark” refers to the background originating from tt and single top quark production. In all cases, the pre-dicted and observed yields show good agreement. Distributions for two benchmark models of chargino-neutralino production, and one of direct left-handedτepair production, are overlaid. The ratio of signal to background is expected to be small for these selections. The numbers within parentheses in the legend correspond to the masses of the parent SUSY particle and the
e
17
6
Systematic uncertainties
We rely on control samples in data in various ways for the estimation of the major backgrounds in the analysis. The dominant uncertainties affecting these estimates are therefore often statis-tical in nature, driven by the limited event yields in the corresponding control samples. For the estimates that rely on simulation, we also propagate systematic uncertainties correspond-ing to the different corrections that are applied, as well as statistical uncertainties related to the limited size of simulated samples. A more detailed discussion of the assessment of systematic uncertainties affecting the individual background sources follows.
In the τhτhfinal state, we rely on an extrapolation in the τhisolation to obtain an estimate of the
background with misidentified τhcandidates. The uncertainty in this extrapolation is driven by
the uncertainty introduced by the dependence of the isolation on the jet flavor. It also includes the statistical uncertainty in the control regions from which this extrapolation is measured. The uncertainty in the identification and isolation efficiency for prompt τhcandidates is also
prop-agated to the final estimate. Finally an additional uncertainty is assessed for the fact that the extrapolations for both τh candidates are correlated, leading to an overall systematic uncer-tainty of 30–37% for this background estimate, depending on the SR. In the estimation of the background from jets misidentified as τhin the eτhand µτhfinal states, for which the transfer
factor is estimated in a W+jets control sample, the purity of this control sample is≈85%, and the remaining≈15% is propagated as a systematic uncertainty. A systematic uncertainty of up to 5% is considered for the rate of leptons misidentified as τh candidates in the leptonic final
states.
The effects of different sources of uncertainty, such as uncertainties related to the jet energy scale; unclustered energy contributing to pmiss
T ; and muon, electron, and τh energy scales that
affect the simulated event samples used in the evaluation of the transfer factor are also prop-agated to the final background estimate. In the eµ final state, the largest source of uncertainty in the estimation of the background with misidentified leptons is the contamination from other background processes in the control regions A, C, and D used for the background estimation. While the C and D regions are quite pure in QCD multijet events (>90%), the level of contam-ination can be as high as ≈45% in the A region. A 50% uncertainty is assigned to the QCD multijet background prediction in this final state to cover the potential effects of this contami-nation.
We rely mostly on simulation to obtain estimates of the other background contributions and the signal yields. We propagate uncertainties related to the b tagging, trigger, and selection efficiencies, renormalization and factorization scale uncertainties, PDF uncertainties, and un-certainties in the jet energy scale, jet energy resolution, unclustered energy contributing to pmissT , and the energy scales of electrons, muons, and τh. For the DY+jets background, we have an
ad-ditional uncertainty related to the corrections applied to the mass shape and pT distribution,
while for the tt background, we propagate an uncertainty arising from the corrections to the top quark pTspectrum. In the leptonic final states, we derive normalization scale factors for the
DY+jets and tt backgrounds in high-purity control samples. We assess uncertainties in these scale factors arising from the various systematic effects mentioned above and propagate them to the corresponding background estimates. We also monitor the trends of these scale factors by applying a series of selection requirements on the discriminating kinematic variables that are as close as possible to the selections applied in the SRs. In the τhτhfinal state, where the SRs
are selected with stringent criteria applied to kinematic variables, we assign a 20% normaliza-tion uncertainty for the producnormaliza-tion cross secnormaliza-tions of these backgrounds, as well as for other SM processes. In the leptonic final states, an uncertainty of 10% is assigned to the normalization
of rare SM backgrounds to cover potential variations between the different SRs. As the WW background contribution can be sizeable in the leptonic final states and in particular for the eµ final state, a normalization uncertainty of 25% is considered for this contribution. These uncer-tainties have been determined from sideband regions that are defined by the same baseline cuts as those that define the search bins, except considering only those bins of the search variables that are not used in the fit for the signal extraction.
The uncertainty of 2.5% [80] in the integrated luminosity measurement is taken into account in all background estimates for which we do not derive normalization scale factors in dedi-cated data control samples, as well as for signal processes. In the case of the signal models we assign additional uncertainties due to differences between the fast simulation used for the signal models and the full simulation used for the background estimates that affect the pmiss
T
resolution and lepton efficiencies. We also checked the effects of possible mismodeling of the initial-state radiation (ISR), which affects the total transverse momentum (pISRT ) of the system of SUSY particles, for the signal processes by reweighting the pISRT distribution of simulated signal events. This reweighting procedure is based on studies of the transverse momentum of Z bo-son events [81]. However these effects were found to be negligible for our SR definitions. The main systematic uncertainties for the signal models and background estimates are summarized in Table 9.
Table 9: Systematic uncertainties in the analysis for the signal models and the different SM background predictions. The uncertainty values are evaluated separately for each signal model and mass hypothesis studied and are listed as percentages.
Uncertainty (%) Signal Misidentified e/µ/τh DY+jets Top quark backgrounds Rare SM
τhefficiency 5–11 0.1–5 5–10 4–10 0.1–10
Electron efficiency (eµ, eτh) 3 — 3 3 3
Muon efficiency (eµ, µτh) 2 — 2 2 2
Isolation extrapolation (eτh, µτh, τhτh) — 15–35 — — —
Misidentified τhcorrelations (τhτh) — 8–13 — — —
QCD multijet normalization (eµ) — 50 — — —
τhenergy scale (eτh, µτh, τhτh) 0.1–23 — 1–34 0.1–24 0.1–33
Jet energy scale 0.1–45 — 0.5–24 0.5–39 0.1–67
Jet energy resolution 1–4 — 29–61 3–10 11–31
Unclustered energy 0.1–41 — 2–42 0.1–41 0.1–100
Electron energy scale (eµ, eτh) 0.1–22 — 0.5–5 0.1–13 0.1–100
Muon energy scale (eµ, µτh) 0.1–11 — 0.1–18 0.1–11 0.1–100
b tagging 0.5–3 1–4 0.1–3 4–20 0.1–2
Drell-Yan mass and pT — — 0.5–29 — —
Background cross sections — — 2–20 5–20 10–20
Fast vs. full simulation 1–30 — — — —
Integrated luminosity 2.5 — — — 2.5
7
Results and interpretation
The results of the analysis in the τhτhfinal state are summarized in Table 10. The background
estimates for the different SM processes are shown with the full uncertainty, the quadratic sum of the statistical and systematic uncertainties. As discussed in Section 6, the uncertainties in the τhτhfinal state are dominated by the statistical uncertainties in the data control regions and
the number of simulated events produced. These uncertainties are modeled in the likelihood function used for the statistical interpretation of the results with gamma distributions [82]. If there is no event in the control region used to obtain a given background estimate for any SR or no event in the simulated sample surviving the SR selection criteria, then the one standard deviation (s.d.) upper bound evaluated for that background contribution is presented in the table. No significant excess is observed in any of the SRs.
19
Table 10: Final predicted and observed event yields in the three SRs defined for the τhτhfinal
state with all statistical and systematic uncertainties combined. For the background estimates with no event in the corresponding data control region or in the simulated sample after the SR selection, the predicted yield is indicated as being less than the one standard deviation upper bound evaluated for that estimate. The central value and the uncertainties for the total background estimate are then extracted from the full pre-fit likelihood. Expected yields are also given for signal models of direct eτpair production in the purely left- and right-handed scenarios and in the maximally mixed scenario, with theτeandχe
0
1 masses in GeV indicated in
parentheses.
SR1 SR2 SR3
Nonprompt and misidentified τh 0.68+−0.900.68 2.49±1.83 <1.24 Drell-Yan+jets background 0.80+−0.970.80 <0.71 <0.71 Top quark backgrounds 0.02+−0.030.02 0.73±0.31 1.76±0.68 Rare SM processes 0.72±0.38 0.20±0.15 0.20+−0.250.20 Total background 2.22+−1.371.12 4.35+−1.751.53 3.70+−1.521.08 Left (150,1) 1.25±0.40 2.91±0.59 1.53±0.33 Right (150,1) 1.09±0.26 1.27±0.20 0.74±0.17 Mixed (150,1) 1.04±0.22 1.39±0.27 0.92±0.15 Observed 0 5 2
A comparison of the observed data with the background prediction for the search variables pmiss
T and ΣmT is shown for the all-hadronic final state in Fig. 4 after the baseline selection.
Similar comparisons are shown for the three search variables pmissT , mT2, and Dζ used in the leptonic final states (eτh, µτh, and eµ) in Figs. 5–7. The background estimates derived for all the
SRs in the leptonic final states, as defined in Tables 4 and 5, together with their uncertainties, are used as inputs to a simultaneous maximum likelihood fit to the observed data. The results for the SR bins that are used for the signal extraction in the final statistical interpretation procedure are shown in Figs. 8–10. Both histograms before the simultaneous fitting of all SRs (pre-fit) and after fitting (post-fit) are shown. The numbers of expected and observed events in each SR are also reported in Tables 12–14 in Appendix A.
No significant deviations from the expected SM background are observed in this search. The results are interpreted as limits on the cross section for the production of τepairs in the con-text of simplified models. The produced τeis assumed to always decay to a τ lepton and a
e
χ01. The 95% confidence level (CL) upper limits on SUSY production cross sections are
cal-culated using a modified frequentist approach with the CLs criterion [83, 84] and asymptotic
approximation for the test statistic [82, 85]. Since the cross section of directeτpair production and the τ lepton decay are strongly dependent on chirality, the results are shown for three different scenarios. Figures 11-13 show the cross section upper limits obtained foreττe produc-tion for the left-handed, maximally mixed, and right-handed scenarios as a funcproduc-tion of theτe mass for different χe
0
1 mass hypotheses, namely 1, 10, 20, 30, 40, and 50 GeV. It can be seen
that the constraints are reduced for higherχe
0
1 masses due to the smaller experimental
accep-tance. The stronger than expected limits observed at loweτmass values for aχe
0
1mass of 50 GeV
in the purely left- and right-handed scenarios are driven by a deficit in the µτh final state in
the 0–jet category, leading to strong constraints on the predicted background contribution in SRs sensitive to these signal models. The extremely smalleττeproduction cross sections make this scenario in general very challenging. This analysis is most sensitive to scenarios with a
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Observed Top quark
(1) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ DY+jets (175) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ Jet →τh (1) 0 1 χ∼ (90), L τ∼ Other SM [GeV] miss T p 2 10 103 Obs. / MC 1 2 Syst. unc. (13 TeV) -1 35.9 fb CMS Entries / 10 GeV 1 − 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 h
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(1) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ DY+jets (175) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ Jet →τh (1) 0 1 χ∼ (90), L τ∼ Other SM [GeV] T m Σ 50 100 150 200 250 300 Obs. / MC 1 2 Syst. unc. (13 TeV) -1 35.9 fb CMS
Figure 4: Distributions of the search variables pmissT (left) and ΣmT (right) for the τhτh final
state for events after the baseline selection. The black points show the data. The background estimates are represented with stacked histograms. Distributions for two benchmark models of chargino-neutralino production, and one of direct left-handedτepair production, are overlaid. The numbers within parentheses in the legend correspond to the masses of the parent SUSY particle and the χe
0
1 in GeV for these benchmark models. In both cases, the last bin includes
overflows.
left-handedτeand a nearly masslessχe
0
1, in which we exclude production rates larger than 1.26
(1.34) times the expected SUSY cross section for aeτmass of 90 (125) GeV.
We also interpret the results as exclusion limits in simplified models of mass-degenerate chargino-neutralino (χe
±
1 χe
0
2) and chargino pair (eχ
±
1 χe
∓
1) production with decays to τ leptons in the final
state via the decay chainsχe ± 1 → eτντ/eνττ → τντχe 0 1,χe 0 2 → ττe→ ττχe 0
1. Equal branching
frac-tions are assumed for each of the two possibleχe ±
1 decay chains considered. Theτeandeντmasses are assumed to be degenerate in these models and to have a value halfway between the mass of the parent sparticles and theχe
0
1mass. Figure 14 shows the 95% CL exclusion limits in the mass
plane ofχe ± 1/χe 0 2versusχe 0
1mass obtained for theχe ± 1 χe 0 2scenario. We excludeχe ± 1/χe 0 2masses up
to around 710 GeV for a nearly massless χe
0
1 hypothesis in this scenario. Figure 15 shows the
corresponding limits for theχe ±
1 χe
∓
1 signal scenario in the plane of χe ± 1 versus χe 0 1 mass. In this scenario, we excludeχe ±
1 masses up to around 630 GeV for a nearly masslessχe
0
1hypothesis.
In order to simplify the reinterpretation of the results obtained in the leptonic final states using other signal models, we define a small set of aggregate SRs by combining subsets of the SRs. These aggregate SRs are chosen to have sensitivity to a range of signal models. Since they are not exclusive, the results obtained for these aggregate SRs cannot be statistically combined. These results are tabulated in Table 11.
21 Entries / bin 1 − 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 h
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e
Observed Top quark
(1) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ DY+jets (175) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ Jet →τh (1) 0 1 χ∼ (90), L τ∼ Other SM [GeV] miss T p 2 10 103 Obs. / MC 1 2 Syst. unc. (13 TeV) -1 35.9 fb CMS µτh Entries / bin 1 − 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 h
τ
e
Observed Top quark
(1) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ DY+jets (175) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ Jet →τh (1) 0 1 χ∼ (90), L τ∼ Other SM [GeV] T2 m 2 10 103 Obs. / MC 1 2 Syst. unc. (13 TeV) -1 35.9 fb CMS µτh Entries / bin 1 − 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 h
τ
e
Observed Top quark
(1) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ DY+jets (175) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ Jet →τh (1) 0 1 χ∼ (90), L τ∼ Other SM [GeV] ζ D 400 − −200 0 200 400 600 800 1000 Obs. / MC 1 2 Syst. unc. (13 TeV) -1 35.9 fb CMS h τ µ
Figure 5: Distributions of the search variables pmissT (top left), mT2(top right), and Dζ (bottom) for the eτhfinal state for events after the baseline selection. The black points show the data. The
background estimates are represented with stacked histograms. Distributions for two bench-mark models of chargino-neutralino production, and one of direct left-handedτepair produc-tion, are overlaid. The numbers within parentheses in the legend correspond to the masses of the parent SUSY particle and theχe
0
1in GeV for these benchmark models. In all cases, the last
Entries / bin 1 − 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 h
τ
µ
Observed Top quark
(1) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ DY+jets (175) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ Jet →τh (1) 0 1 χ∼ (90), L τ∼ Other SM [GeV] miss T p 2 10 103 Obs. / MC 1 2 Syst. unc. (13 TeV) -1 35.9 fb CMS Entries / bin 1 − 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 h
τ
µ
Observed Top quark
(1) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ DY+jets (175) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ Jet →τh (1) 0 1 χ∼ (90), L τ∼ Other SM [GeV] T2 m 2 10 103 Obs. / MC 1 2 Syst. unc. (13 TeV) -1 35.9 fb CMS Entries / bin 1 − 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 h
τ
µ
Observed Top quark
(1) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ DY+jets (175) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ Jet →τh (1) 0 1 χ∼ (90), L τ∼ Other SM [GeV] ζ D 400 − −200 0 200 400 600 800 1000 Obs. / MC 1 2 Syst. unc. (13 TeV) -1 35.9 fb CMS
Figure 6: Distributions of the search variables pmissT (top left), mT2(top right), and Dζ (bottom) for the µτhfinal state for events after the baseline selection. The black points show the data. The
background estimates are represented with stacked histograms. Distributions for two bench-mark models of chargino-neutralino production, and one of direct left-handedτepair produc-tion, are overlaid. The numbers within parentheses in the legend correspond to the masses of the parent SUSY particle and theχe
0
1in GeV for these benchmark models. In all cases, the last
23 Entries / bin 1 − 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10
µ
e
Observed Top quark
(1) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ WW+jets (175) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ QCD multijet (1) 0 1 χ∼ (90), L τ∼ Other SM [GeV] miss T p 2 10 103 Obs. / MC 1 2 Syst. unc. (13 TeV) -1 35.9 fb CMS Entries / bin 1 − 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10
µ
e
Observed Top quark
(1) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ WW+jets (175) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ QCD multijet (1) 0 1 χ∼ (90), L τ∼ Other SM [GeV] T2 m 2 10 103 Obs. / MC 1 2 Syst. unc. (13 TeV) -1 35.9 fb CMS Entries / bin 1 − 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10
µ
e
Observed Top quark
(1) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ WW+jets (175) 0 1 χ∼ (400), 0 2 χ∼ / ± 1 χ∼ QCD multijet (1) 0 1 χ∼ (90), L τ∼ Other SM [GeV] ζ D 400 − −200 0 200 400 600 800 1000 Obs. / MC 1 2 Syst. unc. (13 TeV) -1 35.9 fb CMS
Figure 7: Distributions of the search variables pmissT (top left), mT2(top right), and Dζ (bottom) for the eµ final state for events after the baseline selection. The black points show the data. The background estimates are represented with stacked histograms. Distributions for two bench-mark models of chargino-neutralino production, and one of direct left-handedτepair produc-tion, are overlaid. The numbers within parentheses in the legend correspond to the masses of the parent SUSY particle and theχe
0
1in GeV for these benchmark models. In all cases, the last
![Table 4: Definition of SRs in the 0-jet category for the eτ h and µτ h final states. Bin name p miss T [GeV] m T2 [GeV] D ζ [GeV]](https://thumb-eu.123doks.com/thumbv2/9libnet/4588707.84649/10.892.255.643.522.996/table-definition-category-final-states-gev-gev-gev.webp)
![Table 5: Definition of SRs in the 1-jet category for the eτ h and µτ h final states. Bin name p miss T [GeV] m T2 [GeV] D ζ [GeV]](https://thumb-eu.123doks.com/thumbv2/9libnet/4588707.84649/11.892.258.640.420.936/table-definition-category-final-states-gev-gev-gev.webp)
![Table 6: Definition of SRs in the 0-jet category for the eµ final state. Bin name p miss T [GeV] m T2 [GeV] D ζ [GeV]](https://thumb-eu.123doks.com/thumbv2/9libnet/4588707.84649/12.892.256.641.431.928/table-definition-category-final-state-gev-gev-gev.webp)
![Table 7: Definition of SRs in the 1-jet category for the eµ final state. Bin name p miss T [GeV] m T2 [GeV] D ζ [GeV]](https://thumb-eu.123doks.com/thumbv2/9libnet/4588707.84649/13.892.256.638.430.928/table-definition-category-final-state-gev-gev-gev.webp)
